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A quadrilateral is a plane or 2d figure with four sides.
A 3d shape (object) has a name ending with -hedron, eg a tetrahedron which is a four sided 3d shape.
A 3d quadrilateral has no meaning.
Sides (edges) do exist in 3d shapes, but a more pertinent attribute is faces.
Do you mean by "3d quadrilateral" a 3d shape which has a quadrilateral as a base and at most 4 or 5 other sides, ie a pentahedron (usually called a square pyramid) or a hexahedron (some types of which are called cuboids and cubes)?
Please re-ask using consistent terminology, eg What is a 3d shape with one pair of parallel faces and 6 faces?
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Is a rectangle a quadrilateral with exactly one pair of parallel sides?
It is a quadrilateral with exactly 2 pairs of parallel sides.
What is a quadrilateral with one pair of parallel sides?
A quadrilateral with one pair of parallel sides is called a trapezium (most of the world) or trapezoid (US) . If it was to have two pairs of parallel sides it would be a parallelogram.
If one pair of opposite sides of a quadrilateral is parallel and then the quadrilateral is a parallelogram?
Then, the opposite sides are congruent.
What quadrilateral that only has one pair of parallel sides?
a hexagon
Which quadrilateral shape has one pair of parallel sides?
a trapezoid has
